What is the value of cos((3pi)/5)cos((7pi}{30})-sin((3pi)/5)sin(\frac{7pi)/(30)) ?

The value of cos((3pi)/5)cos((7pi}{30})-sin((3pi)/5)sin(\frac{7pi)/(30)) is -(sqrt(3))/2

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cos((3pi)/5)cos((7pi}{30})-sin((3pi)/5)sin(\frac{7pi)/(30))

cos (\frac{3 π}{5}) cos (\frac{7 π}{30}) - sin (\frac{3 π}{5}) sin (\frac{7 π}{30})

- \frac{3}{2}

Solution steps

cos (\frac{3 π}{5}) cos (\frac{7 π}{30}) - sin (\frac{3 π}{5}) sin (\frac{7 π}{30})

Rewrite using trig identities:

cos (\frac{5 π}{6})

= cos (\frac{5 π}{6})

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

= - \frac{3}{2}

- \frac{1}{4} csc (2 (- \frac{π}{2})^{2})

sec (\frac{π}{16})

1.125 sin (1.125) - 1

\frac{4.5}{cos ( 5 4 ^{\circ} )}

cos (arccos (0.5))

What is the value of cos((3pi)/5)cos((7pi}{30})-sin((3pi)/5)sin(\frac{7pi)/(30)) ?
The value of cos((3pi)/5)cos((7pi}{30})-sin((3pi)/5)sin(\frac{7pi)/(30)) is -(sqrt(3))/2